Table of Contents

1 Finite-Difference Equations.- 1.1 A Mythical Field.- 1.2 The Linear Finite-Difference Equation.- 1.3 Methods of Iteration.- 1.4 Nonlinear Finite-Difference Equations.- 1.5 Steady States and Their Stability.- 1.6 Cycles and Their Stability.- 1.7 Chaos.- 1.8 Quasiperiodicity.- 2 Boolean Networks and Cellular Automata.- 2.1 Elements and Networks.- 2.2 Boolean Variables, Functions, and Networks.- 2.3 Boolean Functions and Biochemistry.- 2.4 Random Boolean Networks.- 2.5 Cellular Automata.- 2.6 Advanced Topic: Evolution and Computation.- 3 Self-Similarity and Fractal Geometry.- 3.1 Describing a Tree.- 3.2 Fractals.- 3.3 Dimension.- 3.4 Statistical Self-Similarity.- 3.5 Fractals and Dynamics.- 4 One-Dimensional Differential Equations.- 4.1 Basic Definitions.- 4.2 Growth and Decay.- 4.3 Multiple Fixed Points.- 4.4 Geometrical Analysis of One-Dimensional Nonlinear Ordinary Differential Equations.- 4.5 Algebraic Analysis of Fixed Points.- 4.6 Differential Equations versus Finite-Difference Equations.- 4.7 Differential Equations with Inputs.- 4.8 Advanced Topic: Time Delays and Chaos.- 5 Two-Dimensional Differential Equations.- 5.1 The Harmonic Oscillator.- 5.2 Solutions, Trajectories, and Flows.- 5.3 The Two-Dimensional Linear Ordinary Differential Equation.- 5.4 Coupled First-Order Linear Equations.- 5.5 The Phase Plane.- 5.6 Local Stability Analysis of Two-Dimensional, Nonlinear Differential Equations.- 5.7 Limit Cycles and the van der Pol Oscillator.- 5.8 Finding Solutions to Nonlinear Differential Equations.- 5.9 Advanced Topic: Dynamics in Three or More Dimensions.- 5.10 Advanced Topic: Poincaré Index Theorem.- 6 Time-Series Analysis.- 6.1 Starting with Data.- 6.2 Dynamics, Measurements, and Noise.- 6.3 The Mean and Standard Deviation.- 6.4 Linear Correlations.- 6.5Power Spectrum Analysis.- 6.6 Nonlinear Dynamics and Data Analysis.- 6.7 Characterizing Chaos.- 6.8 Detecting Chaos and Nonlinearity.- 6.9 Algorithms and Answers.- Appendix A A Multi-Functional Appendix.- A.1 The Straight Line.- A.2 The Quadratic Function.- A.3 The Cubic and Higher-Order Polynomials.- A.4 The Exponential Function.- A.5 Sigmoidal Functions.- A.6 The Sine and Cosine Functions.- A.7 The Gaussian (or “Normal”) Distribution.- A.8 The Ellipse.- A.9 The Hyperbola.- Exercises.- Appendix B A Note on Computer Notation.- Solutions to Selected Exercises.

Promotional Information

Springer Book Archives

Reviews

ANot only are many of the most recent topics included and simply explained, but the reader is also warned against difficulties in the practical implementation of the proposed methods of analysis and against common misinterpretations of some theoretical concepts. Because of its completeness and plain, but mathematically correct, style, this book is also an ideal starting point for researchers from various disciplines who are not familiar with mathematical concepts usually learned in the first two years of university study.A AMATHEMATICAL REVIEWS AI recommend this book strongly both to those who need to teach these topics and to those who want to learn about them, whether or not they are in the biosciences. In fact, I would strongly recommend this book to paleontologists, paleobiologists, paleoecologists, and geologists who are (finally) becoming interested in nonlinear dynamics, but are still afraid to ask.AAAMERICAN SCIENTIST A[The authors] have written a readily accessible introduction to nonlinear dynamicsAthe book presents the main concepts and applications of nonlinear dynamics at an elementary levelAInterspersed in the text are delightful short essays of a page or two eachACourses on nonlinear dynamics rarely present these topics at the level used in the bookAIt is written in a Auser friendlyA colloquial style and is a delight to readAno reader is likely to encounter a more accessible elementary introduction to nonlinear dynamics.AAPHYSICS TODAY

??Not only are many of the most recent topics included and simply explained, but the reader is also warned against difficulties in the practical implementation of the proposed methods of analysis and against common misinterpretations of some theoretical concepts. Because of its completeness and plain, but mathematically correct, style, this book is also an ideal starting point for researchers from various disciplines who are not familiar with mathematical concepts usually learned in the first two years of university study.?? ??MATHEMATICAL REVIEWS ??I recommend this book strongly both to those who need to teach these topics and to those who want to learn about them, whether or not they are in the biosciences. In fact, I would strongly recommend this book to paleontologists, paleobiologists, paleoecologists, and geologists who are (finally) becoming interested in nonlinear dynamics, but are still afraid to ask.????AMERICAN SCIENTIST ??[The authors] have written a readily accessible introduction to nonlinear dynamics??the book presents the main concepts and applications of nonlinear dynamics at an elementary level??Interspersed in the text are delightful short essays of a page or two each??Courses on nonlinear dynamics rarely present these topics at the level used in the book??It is written in a ??user friendly?? colloquial style and is a delight to read??no reader is likely to encounter a more accessible elementary introduction to nonlinear dynamics.????PHYSICS TODAY